On 21 Jan 2009, at 05:46, Kim Jones wrote:
>>
>> OK. But keep in mind that consciousness is unique in the sense of
>> knowing that it cannot know its Turing emulability level (yet can
>> bet).
>>
>>
>>
>
> Footnote - (parenthetical digression): I know the above thought is
> native to your schema, and up to here Penrose appears to agree with
> you.
Penrose has been wrong on this issue in its first book (The Emperor
New clothes), and corrected it formally in the second book "The
Shadows of the Mind". But, he is still incorrect on his general
conclusion drawn from Gödel.
> But, this very singular quality of consciousness (to not know its
> emulability level but to be able to bet on it - via the Bayesian
> probabilities detector that is the mind) is precisely the reason
> Penrose and Hammeroff have decided that the mind is NOT computation;
> because of the uncomputability of this issue.
The fact that we cannot known which machine we are does not prevent us
to be a machine, on the contrary. Note that Penrose and Hammeroff have
split their mind on this issue. Indeed Penrose argues that we are not
machine at all, where Hammeroff can conceive that we are quantum
machine (and in that case comp is satisfied).
In general the non computability argument is wrong because
computationalism explains why many things ABOUT machines are not
computable. The universal machine "lives" on the frontier between the
computable and the non computable.
Note that Penrose, Maudlin and me, do agree that mind and matter
cannot be both computable. But for different reasons, and Penrose's
one are not correct.
> Why should the mind be limited to the computable?
This sentence is ambiguous. In a sense, the comp hyp. makes the mind
"computable" (Turing-emulable), yet it does not necessarily limit the
mind to the computable (angels can think!), nor does it prevents many
manifestation of the mind to be completely not computable. We will
have the opportunity to dig a bit more on this.
By "angel" I mean a self-referential entity not emulable by a machine
(this exists mathematically).
> Clearly it is not. Could an AI conceive of Platonia?
?
Could *you* conceive of Platonia? If yes, then at least one AI can
conceive of Platonia: you (assuming comp of course).
> Now that would perhaps be to go one better than any Blade Runner-
> style Turing Test!
This address the question: "could a machine convinces another that it
conceives of Platonia". This asks for an infinite Turing test indeed.
Well ... even a *big* infinity ... (depending on the precise sense you
can give to "conceive").
> For Penrose, Goedel's Incompleteness Theorem is enough to lock the
> door against the thought that the mind is limited to the algorithms
> of the computable.
It is worse than that. Penrose believes that the mind needs an actual
non computable components. His argument is just wrong. Many logicians
have pinpoint on the mistakes made by Penrose. They are analog of the
errors made by Lucas an half century before. Judson Webb wrote a
formidable book on that issue (ref in the biblio of my Lille thesis).
> The mind, apparently, can understand things outside the realm of the
> computable. I guess it all depends on what you mean by "understand".
> I would cite musical understanding as an example of something that
> cannot be computed. There is information that appears in the
> (listening) mind that cannot be deduced from the notes, the
> melodies, the harmonies, the rhythms etc. All of the mechanics of
> music are of course computable, but my subjective interaction with a
> particular musical discourse is (probably) not.
Universal machines can grasp that there are many things that they
cannot grasp. Penrose, like Lucas and the few people who still believe
that Gödel incompleteness theorem does limit the power of machine,
always forget that some machines can understand and prove that
theorem, even about themselves. Godel's (incompleteness theorem)
really shows how far a machine, betting on its own consistency, can
study its own limitations.
Soon or later, any correct universal machine discover that "its
physical world" is a product of that productive ignorance, and this
without going into solipsism.
>>>
>>> Our world may be a giant hologram - space - 15 January 2009 - New
>>> Scientist
>>
>>
>> Very interesting! Thanks.
>> If consciousness is gravity (the wave selector), as Penrose find
>> plausible, the blurriness of the hologram could necessarily
>> (asuming comp) prevent the observation of the gravitational waves,
>> making them definitely undetectable. Just thinking aloud.
>
>
>
> Isn't this like the Turing lock-out with respect to truth and
> provability?
This is what I was alluding too, from Penrose's curious intuition that
consciousness has something to do with gravity.
> We "know" the gravitational waves are there, but we can never
> directly detect them. Perhaps our "knowing" such a thing is non-
> computable?
If you accept to define, like Theaetetus, knowledge by true belief,
and (scientific) belief by Godel's provability, then it is a theorem
that the "knowing of the machine M" is even not definable by the
machine M. But a machine M can know "the knowing" of a simpler
machine, and then, betting on its own correctness, can lift the
"knower's logic" of the simple machine to its own. That is what makes
theology accessible by machines, both intuitively (knowing) and
scientifically (proving).
Have a good day,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Jan 22 2009 - 05:08:52 PST